1. Field of the Invention
The present invention relates to a method of transmitting a plurality of modulated signals, obtained by modulating a plurality of carrier waves having frequencies with respective transmission signals and multiplexed to produce an input signal by frequency division multiplexing, to a synchronous detector (or a coherent detector), in which synchronous detection is performed to extract the transmission signal, corresponding to each modulated carrier wave of the input signal, from the input signal by calculating a moving average of the input signal every sampling period of time and performing an addition and subtraction calculation, corresponding to the cycle of the corresponding carrier wave, for the moving averages to obtain a level of the transmission signal.
The present invention also relates to a physical quantity detector for detecting a physical quantity by using this method.
2. Description of Related Art
For the transmission of a plurality of transmission signals multiplexed by frequency division multiplexing (FDM) or orthogonal frequency division multiplexing (OFDM), a plurality of carrier waves having different frequencies are modulated with the respective transmission signals to obtain modulated signals, and these modulated signals are multiplexed to produce an input signal in FDM or OFDM. This input signal is transmitted to a synchronous detector. In this detector, the synchronous detection is performed to extract the transmission signal, corresponding to each modulated carrier wave of the input signal, from the input signal.
When the synchronous detector is structured by analog circuits having operational amplifiers and analog filters, one analog circuit is required to extract one transmission signal from each modulated carrier wave. Therefore, the detector requires a large number of analog circuits, so that it is difficult to manufacture a small-sized detector. Further, the analog circuits are easily influenced by external noise, so that it is difficult to reproduce the transmission signals in the detector with high precision. Therefore, the use of the detector is limited to specific environments substantially having no external noises.
Because of the demerits of analog circuits in the synchronous detector, the synchronous detector is structured by digital circuits. For example, Published Japanese Patent First Publication No. 2005-102129 proposes a synchronous detector, structured by digital circuits, in which synchronous detection is performed to extract a transmission signal, corresponding to each modulated carrier wave of an input signal, from the input signal.
In this detector, a sampling period of time is defined to be equal to a half (or a quarter) of the cycle of the reference carrier wave having the highest frequency among carrier waves, and the moving average of the input signal is calculated every sampling period. Then, an addition and subtraction calculation corresponding to the cycle of each carrier wave is performed for the moving averages to extract the corresponding transmission signal from the input signal. More specifically, first moving averages calculated in the first half of the cycle of the carrier wave (i.e., positively oscillating phase range of carrier wave) are added to one another to obtain a summed value, and second moving averages calculated in the latter half of the cycle of the carrier wave (i.e., negatively oscillating phase range of carrier wave) are subtracted from the summed value to obtain a modulation result corresponding to the level of the corresponding transmission signal. Therefore, the transmission signals are extracted from the input signal.
To extract the transmission signals from the input signal in this detector, it is required to set frequencies of the carrier waves at ½n (n=0,1,2, - - - ,N; N is a positive integer) of the reference frequency (i.e., the highest frequency) of the reference carrier wave. To calculate the moving averages of the input signal, the synchronous detector has a time analog-to-digital (A/D) converter with a pulse delay circuit, and this circuit has a series of delay units. Therefore, the detector can be structured without using any analog circuits such as operational amplifiers and analog filters and can simultaneously perform the synchronous detection to extract the transmission signal, corresponding to each modulated carrier wave of the input signal, from the input signal.
In this detector, each moving average inevitably has an error. Further, as the frequency of the carrier wave becomes lower, the number of moving averages for the addition and subtraction calculation in one cycle of the carrier wave is increased. Therefore, when a transmission signal is superimposed onto a carrier wave having a low frequency, errors of the moving averages added and subtracted in the calculation corresponding to the cycle of the carrier wave are effectively cancelled out. In this case, the error in the voltage level of the transmission signal extracted from the input signal becomes small, and the transmission signal can be extracted using the synchronous detection with high precision.
However, as the frequency of the carrier wave becomes higher, the number of moving averages for the addition and subtraction calculation in one cycle of the carrier wave is decreased. Therefore, when a transmission signal is superimposed onto a high frequency carrier wave, errors in the moving averages added and subtracted in the calculation corresponding to the cycle of the carrier wave are not effectively cancelled out. In this case, the error in the voltage level of the transmission signal extracted from the input signal becomes large, so that the precision of the transmission signal extracted in the synchronous detection is inevitably lowered.
More specifically, in the time A/D converter of the pulse delay circuit, a pulse signal is transmitted through each of the delay units arranged in series while being delayed in each delay unit, and the delay time in each of the delay units depends on the voltage level of the input signal. A sampling period of time is set to be a half (or a quarter) of the period 1/fc0 of the reference carrier wave having the highest frequency fc0, and the number of delay units, through which the pulse signal is transmitted every sampling period, is counted. One moving average of the input signal is calculated from the counted value obtained every sampling period.
Therefore, each moving average inevitably has an error corresponding to a period of time shorter than the delay time of one delay unit. This error occurring in one moving average is added to the next moving average.
Further, in the synchronous detector, for each carrier wave, the moving averages of the input signal in the first half of one cycle of the carrier wave are added to one another to obtain a summed value, and the moving averages in the latter half of one cycle of the carrier wave are subtracted from the summed value to obtain a demodulation result corresponding to the level of the corresponding transmission signal. Therefore, when the frequency of the carrier wave is low, an adding period of time and a subtracting period of time in one cycle of the carrier wave are long, so that the number of moving averages in each half of the cycle of the carrier wave is increased. In this case, because the addition and subtraction calculations are performed for a large number of successively-calculated moving averages every cycle of the carrier wave, errors in the moving averages are effectively cancelled out every cycle of the carrier wave. Therefore, the synchronous detection for extracting the transmission signal modulating the low frequency carrier wave can be precisely performed.
In contrast, when the frequency of the carrier wave is high, the adding calculations and the subtracting calculations are alternately changed within a short period of time in each cycle of the carrier wave. In this case, an addition period of time and a subtraction period of time in each cycle of the carrier wave are short, so that the number of moving averages added to one another and the number of moving averages subtracted from the summed value every cycle of the carrier wave become low. Therefore, errors of the moving averages in one cycle of the carrier wave are not effectively cancelled out. As a result, the precision in the synchronous detection for extracting the transmission signal modulating the high frequency carrier wave is inevitably lowered.
As described above, in the synchronous detection of the carrier waves having different frequencies, when a transmission signal superimposed onto one carrier wave of a high frequency has a low voltage level so as to have a low signal-to-noise (S/N) ratio, the S/N ratio in the signal demodulated in the synchronous detection is further lowered. Therefore, the transmission signal superimposed onto the carrier wave of the high frequency cannot be reproduced in the demodulation with high precision.
An electrostatic floating type gyro representing a physical quantity detector has been disclosed in each of Published Japanese Patent First Publication No. 2005-140709 and Published Japanese Patent First Publication No. 2005-214948. In this gyro, a gyro rotor electrostatically floats in a gyro case and is can rotate. Two electrostatic electrodes are attached to the case along an x-axis in a pair to apply an electrostatic force on the rotor along the x-axis. The electrostatic capacity between this electrode pair and the rotor is changed in response to the movement of the rotor along the x-axis. In the same manner, a pair of electrostatic electrodes is attached to the case along a y-axis, and three pairs of electrostatic electrodes are attached to the case along a z-axis. The rotor is moved in the case in response to the acceleration applied to the case along each axis, the angular velocity around the x-axis and the angular velocity around the y-axis.
A control voltage is applied to each pair of electrostatic electrodes to hold the rotor at a predetermined position within the case. A carrier wave is also applied to each pair of electrostatic electrodes to be superimposed onto the corresponding control voltage. When an acceleration and an angular velocity are applied to the case, the position of the rotor relative to the case is moved, and the voltage applied to the rotor from each pair of electrostatic electrodes is changed due to a change of the capacitance coupling between the rotor and the pair of electrostatic electrodes. This gyro detects the acceleration and the angular velocity from a change of the voltages applied to the rotor from the pairs of electrostatic electrodes.
However, in this gyro, when the control voltage is superimposed onto one high frequency carrier wave, a displacement detecting signal cannot be received from the rotor with high precision. Especially, when the control voltage is low, the signal-to-noise (S/N) ratio of the displacement detecting signal is further lowered. Therefore, the acceleration and the angular velocity cannot be detected with sufficiently high precision.